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   https://doi.org/10.3390/e24111585  

   Esfarjani, Keivan; Liang, Yuan (November 2022, Entropy)

   In this review, motivated by the recent interest in high-temperature materials, we review our recent progress in theories of lattice dynamics in and out of equilibrium. To investigate thermodynamic properties of anharmonic crystals, the self-consistent phonon theory was developed, mainly in the 1960s, for rare gas atoms and quantum crystals. We have extended this theory to investigate the properties of the equilibrium state of a crystal, including its unit cell shape and size, atomic positions and lattice dynamical properties. Using the equation-of-motion method combined with the fluctuation–dissipation theorem and the Donsker–Furutsu–Novikov (DFN) theorem, this approach was also extended to investigate the non-equilibrium case where there is heat flow across a junction or an interface. The formalism is a classical one and therefore valid at high temperatures. 

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2. Bootstrapping Fisher Market Equilibrium and First-Price Pacing Equilibrium

   Liao, Luofeng; Kroer, Christian (July 2024, ICML 2024)
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4. Modeling colloidal interactions that predict equilibrium and non-equilibrium states

   https://doi.org/10.1063/5.0086650  

   Ryu, Brian K.; Fenton, Scott M.; Nguyen, Tuan T.; Helgeson, Matthew E.; Zia, Roseanna N. (June 2022, The Journal of Chemical Physics)

   Modulating the interaction potential between colloids suspended in a fluid can trigger equilibrium phase transitions as well as the formation of non-equilibrium “arrested states,” such as gels and glasses. Faithful representation of such interactions is essential for using simulation to interrogate the microscopic details of non-equilibrium behavior and for extrapolating observations to new regions of phase space that are difficult to explore in experiments. Although the extended law of corresponding states predicts equilibrium phases for systems with short-ranged interactions, it proves inadequate for equilibrium predictions of systems with longer-ranged interactions and for predicting non-equilibrium phenomena in systems with either short- or long-ranged interactions. These shortcomings highlight the need for new approaches to represent and disambiguate interaction potentials that replicate both equilibrium and non-equilibrium phase behavior. In this work, we use experiments and simulations to study a system with long-ranged thermoresponsive colloidal interactions and explore whether a resolution to this challenge can be found in regions of the phase diagram where temporal effects influence material state. We demonstrate that the conditions for non-equilibrium arrest by colloidal gelation are sensitive to both the shape of the interaction potential and the thermal quench rate. We exploit this sensitivity to propose a kinetics-based algorithm to extract distinct arrest conditions for candidate potentials that accurately selects between potentials that differ in shape but share the same predicted equilibrium structure. The algorithm selects the candidate that best matches the non-equilibrium behavior between simulation and experiments. Because non-equilibrium behavior in simulation is encoded entirely by the interparticle potential, the results are agnostic to the particular mechanism(s) by which arrest occurs, and so we expect our method to apply to a range of arrested states, including gels and glasses. Beyond its utility in constructing models, the method reveals that each potential has a quantitatively distinct arrest line, providing insight into how the shape of longer-ranged potentials influences the conditions for colloidal gelation. 

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5. Sociotechnical stability and equilibrium

   https://doi.org/10.1016/j.cosust.2021.01.003  

   Erbaugh, James T; Callahan, Christopher W; Finger-Higgens, Rebecca; DeSiervo, Melissa; Bolger, Douglas T; Cox, Michael; Howarth, Richard B (April 2021, Current Opinion in Environmental Sustainability)